Here's a chunk from "the book" about it:
2−1−6. SAFETY ALERT
Issue a safety alert to an aircraft if you are aware the
aircraft is in a position/altitude which, in your
judgment, places it in unsafe proximity to terrain,
obstructions, or other aircraft. Once the pilot informs
you action is being taken to resolve the situation, you
may discontinue the issuance of further alerts. Do not
assume that because someone else has responsibility
for the aircraft that the unsafe situation has been
observed and the safety alert issued; inform the
appropriate controller.
NOTE−
1. The issuance of a safety alert is a first priority (see
para2−1−2, Duty Priority) once the controller observes
and recognizes a situation of unsafe aircraft proximity to
terrain, obstacles, or other aircraft. Conditions, such as
workload, traffic volume, the quality/limitations of the
radar system, and the available lead time to react are
factors in determining whether it is reasonable for the
controller to observe and recognize such situations. While
a controller cannot see immediately the development of
every situation where a safety alert must be issued, the
controller must remain vigilant for such situations and
issue a safety alert when the situation is recognized.
2. Recognition of situations of unsafe proximity may result
from MSAW/E−MSAW/LAAS, automatic altitude readouts,
Conflict/Mode C Intruder Alert, observations on a PAR
scope, or pilot reports.
3. Once the alert is issued, it is solely the pilot’s
prerogative to determine what course of action, if any, will
be taken.
a. Terrain/Obstruction Alert. Immediately issue/
initiate an alert to an aircraft if you are aware the
aircraft is at an altitude which, in your judgment,
places it in unsafe proximity to terrain/obstructions.
Issue the alert as follows:
PHRASEOLOGY−
LOW ALTITUDE ALERT (call sign),
CHECK YOUR ALTITUDE IMMEDIATELY.
THE (as appropriate) MEA/MVA/MOCA/MIA IN YOUR
AREA IS (altitude),
or if an aircraft is past the final approach fix
(nonprecision approach),
or the outer marker,
or the fix used in lieu of the outer marker (precision
approach),
and, if known, issue
THE (as appropriate) MDA/DH IS (altitude).
If I was working you from the tower and got an alarm, I'd usually have a look out the window and, unless you were in an unusual attitude for your phase of flight or were coming down like a sack of hammers, I probably wouldn't say anything.
If I was in the radar room, since there's no way to see out, I'd probably issue the alert. Even though you are on a visual approach, it's a tough sell to explain why no alert was issued if, heaven forbid, something happened.
As far as how you should reply when an alert is issued... "roger" always worked just fine for me.